Exact Wave Functions for Generalized Harmonic Oscillators
Nathan Lanfear, Raquel M. Lopez, Sergei K. Suslov
TL;DR
This paper derives exact wave functions for generalized harmonic oscillators by transforming the Schrödinger equation into a standard form, linking classical and quantum dynamics through the Arnold transformation.
Contribution
It provides a method to explicitly construct wave functions for a broad class of quadratic Hamiltonians using Ermakov and Riccati systems, connecting classical and quantum descriptions.
Findings
Exact wave functions expressed via Ermakov and Riccati solutions
Classical Arnold transformation relates to Ehrenfest's theorem
Unified framework for time-dependent quadratic Hamiltonians
Abstract
We transform the time-dependent Schroedinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time-evolution of exact wave functions of generalized harmonic oscillators is determined in terms of solutions of certain Ermakov and Riccati-type systems. In addition, we show that the classical Arnold transformation is naturally connected with Ehrenfest's theorem for generalized harmonic oscillators.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum chaos and dynamical systems · Quantum Mechanics and Non-Hermitian Physics · Nonlinear Photonic Systems